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Manuscript V-B@1 · V-B-v1.tex · lemma · 3fadc1ad

Lemma: Local causal interpretation

Geometry, local interpretation, and analytical continuation · lines 293–306 · proof included or linked

V-B@1#lem:causal

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A developed straight displacement with

Δ T > 0, ∣Δ x ∣ \leq c Δ T

is future causal. At a static port, $d τ = d T$ .

Proof. The tangent inequality is $- c^{2} T ˙^{2} + ∣ x ˙ ∣^{2} \leq 0$ . The proper-time statement follows by setting $x ˙ = 0$ .

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$Δ T > 0, ∣Δ x ∣ \leq c Δ T$

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